序列信息在分子组装最小模型中的作用
The Role of Sequence Information in Minimal Models of Molecular Assembly
AI总结：
本文通过比较带骨架与有序列aTAM，证明几何约束决定有限通用瓦片套件是否存在，从而揭示物理机制对高效利用序列组装信息的关键作用。
摘要：
序列指导的组装过程——例如蛋白质折叠——使得仅用少数几种基本构件就能以高精度组装大量结构。我们旨在通过研究温度为1的抽象瓦片组装模型（aTAM）的变体，探索序列信息能以多高效率指导组装。我们针对每种变体追问：是否存在一个有限的瓦片类型集合，能够确定性地组装给定组装模型可产生的任意形状；我们将此类瓦片类型集合称为“通用组装套件”。我们的第一个模型称为“带骨架aTAM”，它通过强制瓦片按照预定的瓦片类型序列被添加到紧邻前一瓦片的晶格位置，生成骨架辅助组装。我们证明了带骨架aTAM存在通用组装套件，并表明即使在对组装规则施加严格限制的情况下，该集合的存在性仍然保持。我们将这些结果与一个约束较少的模型进行比较，该模型称为有序列aTAM，它同样使用预定的瓦片序列，但不要求瓦片与紧邻的前序瓦片相邻。我们证明，在严格情形下，该模型不存在通用组装套件。鉴于对于一个足够大但有限的瓦片集合，长度为N的瓦片序列数量，其增长速度快于尺寸为N的可产生形状的数量及其最坏情况下的Kolmogorov复杂度，这种套件的缺失令人惊讶。我们的结果表明，物理机制，尤其是几何约束，对于促进结构组装中分子程序信息的高效利用具有重要意义。
英文摘要：
Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence information can be used to direct assembly by studying variants of the temperature-1 abstract tile assembly model (aTAM). We ask whether, for each variant, their exists a finite set of tile types that can deterministically assemble any shape producible by a given assembly model; we call such tile type sets "universal assembly kits". Our first model, which we call the "backboned aTAM", generates backbone-assisted assembly by forcing tiles to be added to lattice positions neighbouring the immediately preceding tile, using a predetermined sequence of tile types. We demonstrate the existence of universal assembly kit for the backboned aTAM, and show that the existence of this set is maintained even under stringent restrictions to the rules of assembly. We compare these results to a less constrained model that we call sequenced aTAM, which also uses a predetermined sequence of tiles, but does not constrain a tile to neighbour the immediately preceding tiles. We prove that this model has no universal assembly kit in the stringent case. The lack of such a kit is surprising, given that the number of tile sequences of length N scales faster than both the number and worst-case Kolmogorov complexity of producible shapes of size N for a sufficiently large - but finite - set of tiles. Our results demonstrate the importance of physical mechanisms, and specifically geometric constraints, in facilitating efficient use of the information in molecular programs for structure assembly.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
